For a system using a single Radeon HD 6850 graphics card AMD specifies a minimum of a 500 Watt or greater power supply. The power supply should also have a combined +12 Volt continuous current rating of 30 Amps or greater and have at least one 6-pin PCI Express supplementary power connector.
Total Power Supply Wattage is NOT the crucial factor in power supply selection!!! Total Continuous Amperage Available on the +12V Rail(s) is the most important factor.
The Corsair Gaming Series GS700 (CMPSU-700G), with its combined +12 Volt continuous current rating of 56 Amps and with two (6+2)-pin PCI Express supplementary power connectors, is more than sufficient to power your system configuration with a single Radeon HD 6850.
I think a Corsair Gaming Series GS500 (CP-9020005-XX), with its combined +12 Volt continuous current rating of 39 Amps and with two (6+2)-pin PCI Express supplementary power connectors, is quite sufficient and $30 cheaper.
The Intel Desktop Board DH61WW has one PCI Express 2.0 x 16 bus add-in card connector so it will support a Radeon HD 6850 just fine.